January 17, 2019

Whither Fragility? Dual Momentum GEM

Corey Hoffstein of Newfound Research recently wrote an article called, “Fragility Case Study: Dual Momentum GEM.” Corey starts out saying my dual momentum approach is the strategy he sees implemented the most among do-it-yourself tactical investors. Corey then said several investors bemoaned that GEM kept them invested in the stock market during the last quarter of 2018. It signaled them out of the S&P 500 at the beginning of January after the market was in a drawdown. This caused them to no longer follow the GEM signals as given.

Corey’s solution is to advocate the use of multiple lookback periods to reduce the chance of “bad luck.” He showed the performance of seven monthly lookback periods ranging from 6 to 12 months. He presented a composite of those lookbacks that create seven different GEM models instead of the usual one with a 12-month lookback.

Corey argued that his approach would reduce specification risk. He says this is important because “performance differences due to model specification are not expected to mean revert and are therefore expected to be random but very permanent return artifacts.”

This may be true over the short-run. You cannot expect poor recent performance to be immediately followed by good performance. (We will ignore the fact that stocks are short-term mean reverting.) But neither can you expect poor performance to follow poor performance. Each monthly return from momentum investing is independent but with a positive expected value. Otherwise, you would not do momentum investing.

Expected Value

Say you flip a coin three times, and it comes up heads every time.  You cannot say what the outcome will be over the next 3 tosses since they are independent. But the law of large numbers says that over time your results will approach 50/50. As you accumulate more coin tosses, your results should converge to the 50/50 expected value of each coin toss.

Let us say you want heads to appear and you have a fair coin with a 50/50 chance of heads coming up. You have another coin that has a 60% chance of heads coming up. You would always want to use the second coin. This is true even though your short-term results might seem random. You wouldn’t split your wagers between the two coins. You would choose the one that gives the best expected results. The same is true with investing. If you have an expected edge from a particular strategy, you should favor that strategy.

You might be able to smooth short-term volatility some by using multiple lookback models, but at what opportunity cost?   Betting red and black simultaneously in roulette will dramatically reduce your variability, but it is not a smart bet. You need to consider expected value as well as diversification.

The crux of Corey’s argument is that all lookbacks are equal, and any differences among them are statistical noise.  So you might as well pool them together and exploit the perceived benefits of diversification. But Corey bases this on only 10 years of past data. The less data you use, the less chance you have of showig statistical significance. For properly determining statistical significance you should use as much data as possible. Corey has access to the same data I do and could have used it for his statistical tests. One has to wonder why he did not do so.

One also needs to wonder why Corey choose a range of lookbacks from 6 to 12 months. He could have chosen a range starting from 3 months which also comes up in momentum studies. Corey's selection bias here further weakens his statistical inferences.

Even if you have plenty of data, it may still be difficult to find statistical significance when comparing Sharpe ratios. This is due to their weak adherence to the usual statistical assumptions. If you are going to compare Sharpe ratios, you should at least use robust estimation methods. But these often produce wide confidence intervals. Not seeing significance could also be due to the low power of these kind of tests. With these, you should also be looking at independent data sets. Corey's seven lookbacks are not independent. They are highly correlated which further invalidates tests of their statistical significance.

Corey also introduces bias by using an equally allocated range of lookbacks. The percentage difference between 6 and 7 is greater than the percentage difference between 11 and 12. This means there will be a greater range of results in the lower lookback periods that will cause overweighting in their direction.

On a practical front, of the seven lookback periods Corey used, only the 10-month one would have gotten you out of the S&P 500 before the December loss. The 8 and 9-month lookbacks would have kept you in then and caused you to miss out on profits in November. The other 3 months would have given the same results as the 12 month lookback. During the last quarter of the year, the 12-month lookback model was down the same amount as the S&P index, 13.6%. With Corey's 7 lookbacks, you would have been down 12.3%. There would have been little difference in the outcome between using one or seven lookback models. To better answer the question if a 12-month lookback is desirable, let us look at the evidence.

History of the 12-Month Lookback

A 12-month lookback with U.S. stocks was first presented by Cowles & Jones in 1937. They tabulated the performance of all NYSE stocks from 1920 through 1935. After examining the data, they concluded stocks that performed better the past 12-months also outperformed the following year. The 12-month lookback they identified has held up well in and out of sample going forward and backwards in time since 1937. Jegadeesh (1990) in "Evidence of Predictable Bahavior of Security Returns" showed that the 12-month serial correlation in stocks was particularly strong compared to other months.

Greyserman & Kaminski (2014) showed that long/short absolute momentum with a 12-month lookback beat buy-and-hold back to the beginning of stock trading in the 1600s. It did better in all markets back to the year 1223!


I do not see how anyone can look at these studies and say, as some do, that momentum with a 12-month lookback is just good luck. Looking at the big picture, you cannot judge the probability of something happening after it has already happened. You have to look at results out-of-sample. A 12-month lookback period has plenty of out-of-sample validation over different time frames and in different markets since it was first introduced by Cowles and Jones in 1937 and validated by Jegadeesh & Titman in 1993.

Lookback period comparisons

The first rigorous comparison of lookback periods was in Jegadeesh & Titman’s (1993) seminal momentum paper. They compared 3, 6, 9, and 12-month formation (lookback) and holding periods on U.S. stocks from 1965 through 1989.

We see an improvement in return and t-stats as we go from a 3 to a 12-month lookback period. Not only does a 12-month lookback show the best performance. The continuity in improvement as we extend the lookback period from 3 to 12-months supports the robustness of the 12-month lookback period.

Absolute (time series) momentum applied to multiple markets from 1985 through 2009 also showed a steady improvement in t-stats as the lookback period increased from 6 to 12 months.

               Source: Moskowitz, Ooi, and Pedersen (2012), “Time Series Momentum

GEM Results

Let us now look at GEM. Here are the results using 3, 6, 9, and 12-month lookback periods and an equally weighted combination of these periods since 1950. The GAA benchmark is a global asset allocation of 45% S&P 500, 28% MSCI ACWI ex-U.S. or World ex-U.S., and 27% 5-Year Bonds. This represents the amount of time GEM was in each of these markets since 1950. (For more on GEM since 1950, see our blogpost "Extended Backtest of Global Equities Momentum.")



GEM 12 GEM 9  GEM 6 GEM 3 Composite GAA
CAGR  15.5  13.9  14.6  12.7  14.3    9.8
Standard Deviation  11.6  11.4  10.9 1 1.0  10.2    9.9
Sharpe        Ratio  0.95  0.83  0.93  0.76  0.95  0.58
Worst Drawdown -17.8 -20.7 -21.6 -23.3 -17.7 -41.2
Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

A 12-month lookback comes closest to that old Wall Street adage, "More money is made by sitting than by trading." Any time you deviate from the market index, you are saying you know more than the market. This can be a dangerous assumption. We prefer to stay as close as we can to a buy-and-hold approach while preserving the benefits of dual momentum.

A 12-month lookback keeps one in stocks longer than shorter lookbacks. Over these 68 years, it outperformed the shorter lookbacks in CAGR, Sharpe ratio, and worst drawdown. It gave an increase of 120 basis points in annual return over the composite of lookback periods and gave the highest terminal wealth. The fact that 12-months also also outperformed with stocks in Jegadeesh & Titman's study of stocks and in in the Marowitz et al. study of 58 futures markets is also evidence of its robustness.

The 12-month and composite lookbacks had the same Sharpe ratio and worst month-end drawdown here. Corey also showed a higher return and equal Sharpe ratio from a 12-month lookback compared to a composite of seven lookbacks over the short 10-year period he examined.

So why not sacrifice 120 basis points in past annual return and use the composite since the Sharpe ratios and drawdowns are the same and short-term volatility is less? There are a several reasons why you may not want to do so.

First is the added complexity from multiple models. GEM was designed for public do-it-yourself investors as something easy to understand and implement. It's hard to imagine public investors wanting to run seven or even four dual momentum models every month.

Next, there are 35% more trades for the composite of four lookbacks in GEM. Shorter lookbacks are less stable than longer ones and may be more susceptible to losses in choppy markets. A 12-month lookback with fewer trades is also more tax efficient. With a 12-month lookback, around 70% of  GEM trades would have given long-term capital gains. This would change with shorter lookback periods. In addition, a 12-month lookback has no seasonality bias.

An Alternative

Outside diversification can reduce the impact of specification risk without harming the expected value of an investment model. If you want to reduce the short-term volatility of GEM, you can add a modest allocation to stocks, bonds and/or other assets instead of using multiple lookbacks. You could also add other strategies.

Here is the composite lookback model compared to simple GEM with a 10% allocation to 5-year bonds. It is in line with Warren Buffett's investment instructions for his estate: 90% S&P index fund and 10% short-term bonds.


Composite GEM 90/10
CAGR    14.3    15.2
Standard Deviation    10.2    10.4
Sharpe         Ratio    0.95    0.95
Worst Drawdown  -17.7   -16.0
Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

Results from adding bonds are better and provide more diversification than using correlated model lookbacks. It is also a more flexible approach. Conservative investors could alter the 90/10 ratio to suit their own risk preferences. In my book I show a 70% allocation to GEM and a 30% allocation to bonds for more conservative investors who want less short-term variability. Allocating to a different asset can reduce style and timing risks, as well as specification risk.

Practicality

GEM was introduced as a way for do-it-yourself investors to use dual momentum. It is much easier to use one rather than seven different lookback models as Corey suggests.

No one can say with certainty what the future will be. Process diversification can be beneficial if it is done selectively.  Corey is correct in saying specification risk exists, and it can be reduced by using mutiple lookback models. But there are other ways, such as outside diversification, to reduce specification and other risks.

I use multiple lookbacks myself in the proprietary dual momentum models I license to investment advisors. But I do not indiscriminately combine them. I found I can enhance performance by using criteria in addition to time in selecting lookback periods. I also succesfully applied dual momentum to the bond market where shorter lookback periods are more effective.

Better Informed Investors


To me, the most interesting idea in Corey’s article was that some investors and advisors overreact to short-term performance. Trend following models will never sell at the top nor buy at the bottom. They do not have to for investors to do well. There will always be noise and tracking error whether you have one or a dozen lookback models.

The real fragility is with investors who misperceive the normal volatility you should expect from momentum investing. If you change or abandon a model whenever it has losing trades, you are less likely to succeed at quantitative investing. Dual momentum investors need a good understanding of the process and the research supporting it. This can help them keep the big picture in mind.

January 1, 2019

Our Most Popular Posts in 2018


Happy New Year! In case you missed them, here are our most popular posts in 2018:


My book had dual momentum results from 1974 through 2013. With the acquisition of additional data, we are now able to show results back to 1950. We also explain why 1950 is a good starting date for looking at global investing.


We show examples of common mispractices in quantitative investing: overfitting of data, indiscriminate data mining, biased perceptions, and paucity of data. Ex-post and ex-ante results are not the same.


These show up regularly and repeatedly on the internet. We discuss stocks versus indices, relative  versus absolute momentum, trend following versus diversification, and trade timing issues.


Guest post by Matt Richarson, JD, PhD. Matt looks at simulated safe withdrawal rates for our popular Global Equities Momentum (GEM) model.

October 16, 2018

Extended Backtest of Global Equities Momentum

In 2013, I created my Global Equities Momentum (GEM) model. It holds U.S. or non-U.S. stock indices when stocks are strong and uses bonds as a safe harbor when stocks are weak.

When my book, Dual Momentum Investing, was published in 2014, I had Barclays bond index data back to 1973. Since one year of data is needed to initialize the GEM model, results went from 1974 through 2013. In 2015, I got access to Ibbotson Intermediate Government bond data. This allowed me to extend GEM back to 1970.

The extra bond data lets us see how GEM performed during the 1973-74 bear market. GEM was up 20% those two years, while the S&P 500 index was down over 40%. This was a short but impressive out-of-sample validation of my dual momentum approach.

I thought 1971 was as far back as I could ever take GEM because MSCI non-U.S. stock index data only went back to 1970. But I recently got access to long-term Global Financial Data (GFD) going back much further.

Global Investing

We want as much data as we can get to confirm an investment strategy. But we also have to consider how realistic our results will be under earlier conditions. Global investing, for example, makes little sense during the two World Wars. In WWI, there were strict capital controls that made it almost impossible to invest globally. These eased up a bit during the 1920s. But they strengthened again during the Great Depression. During WW II, they were the strongest that they had ever been.

Even if you could have invested globally back then, it would have made little sense to do so. Imagine as a U.S. investor you went to a cocktail party and said you bought German, Italian, or Japanese stocks. You would never get invited to another party. As an institutional investor, you would have lost all your clients.

If you had invested globally then, it would have been imprudent to do so. Right after WW II, German stocks lost 91% of their value, and Japanese stocks dropped 97%. Governments did not know how to manage their economies prior to WW II. In the U.S., the government made the Great Depression worse by austerity measures and by not having social safety nets or safeguards like the FDIC to protect the public. The continued decline in stock prices after the intial drop was largely due to policy failures unlikely to be repeated now.


Source: Dimson, Marsh & Staunton, Triumph of the Optimists:101 Years of Global Investment Returns, Princeton University Press, 2002

So, what is a good starting date for global investing? The first academic paper to point out the benefits of international investing was in 1968 [1]. There were similar papers in 1970 and 1974 [2]. The first mutual fund to make global investing available to U.S. investors was the Templeton Growth Fund that began in 1954. Asness, Israelov, and Liew (2017) in “International Diversification Works (Eventually)” begin their study in 1950 using GFD data. This seems to be a reasonable starting time. So GEM results will begin on January 1950.

Data Sources

We use the S&P 500 index for U.S. stocks. For non-U.S. stocks, we use the MSCI All Country World Index ex-U.S. from its start date in January 1989. It includes both developed and emerging markets. By using as broad an index as possible, we avoid selection bias. Before 1989, we use the MSCI World Index ex-U.S. from its start date in January 1970, and the GFD World Index ex-U.S. before then. For bonds, we use the Barclays U.S. Aggregate Bond Index from its start in January 1973. Before 1973, we use the Ibbotson Intermediate Government Index of 5-year bonds.

GEM Model

Geczy & Samonov (2015) show that momentum consistently outperformed buy-and-hold back to the year 1801. Momentum applied to geographically diversified stock indices outperformed momentum applied to stocks, bonds, commodities, currencies, and sectors.  That is how we use momentum.

When the trend of stocks is up according to absolute momentum applied to the S&P 500, we use relative strength to determine if we will be in U.S. or non-U.S. stocks. When the trend of stocks is down, we invest in bonds. We use a 12-month look back period for both types of momentum and rebalance monthly.

You cannot judge the probability of something happening after it has already happened. You have to look at results out-of-sample. A 12-month look back was first introduced in Cowles & Jones' 1937 study of momentum. It also worked best in the Jegadeesh & Titman (1993) seminal study on relative momentum and in the Moskowitz et al. (2012) seminal study on absolute (time series) momentum.

A 12-month momentum look back soundly beat buy-and-hold from the beginning of stock market trading in the 1600s and when applied to other assets back to 1223 as reported by Greyserman & Kaminski (2014).

Tobias Moskowitz, a respected momentum researcher, said, "Momentum is a phenomenon that exists at 6 to 12 month horizons." [3] Most academic papers on stock market momentum use a 6 or 12 month lookback.

We prefer 12-months because there is the most out-of-sample evidence supporting it. It also has fewer trades and is more tax efficient than shorter lookbacks.

GEM Results

Here are GEM results compared to a global asset allocation (GAA) benchmark of 45% in U.S. stocks, 28% in non-U.S. stocks, and 27% in 5-year bonds. These percentages represent the amount of time GEM spent in each of these markets. It also represents a typical global asset allocation portfolio.

                                           Jan 1950- Sep 2018     Jan 1950- Dec 1979    Jan 1980- Sep 2018


 GEM
GAA
GEM
GAA
GEM
GAA
CAGR
   15.8
   10.0
  13.9
    9.6
   17.3
  10.3
Annual Std Dev
   11.5
    9.8
  10.2
    8.3
  12.4
  10.9
Skewness
-0.09
-0.54
 0.30
-0.24
-0.29
-0.63
Sharpe Ratio
 0.96
 0.57
 0.72
 0.39
 1.03
 0.58
Worst Drawdown
-17.8
-41.2
-15.8
-29.3
-17.8
-41.2
Worst 6 Months
-15.7
-33.0
-15.7
-21.0
-15.0
-33.0
Worst 12 Months
-17.8
-35.7
-13.3
-28.1
-17.8
-35.7
% of Profit Months
   69
   67
   67
   68
    72
    63

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.




Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

The correlation in monthly returns between GEM and GAA is 0.60 and between GEM, and the S&P 500 is 0.50.  There were on average only 1.5 trades per year with GEM. So transaction costs would have been minimal.

These results are updated monthly on the Performance pages of my website.

Relative versus Absolute Momentum


To better understand what is going on with GEM, I separated out its two components, relative and absolute momentum.


GEM
REL MOM
ABS MOM
S&P 500
CAGR
  15.8
  13.4
  12.3
  11.4
Annual Std Dev
  11.5
  14.4
  11.2
  14.2
Sharpe Ratio
 0.96
 0.64
 0.70
 0.52
Worst Drawdown
-17.8
-54.6
-29.6
-51.0
Worst 6 Months
-15.7
-41.8
-25.2
-41.8
Worst 12 Months
-17.8
-48.1
-25.3
-43.3
% of Profit Months
   69
   65
   67
   64

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

Relative momentum is where we switch between U.S. and non-U.S. stocks based on relative strength. Relative momentum still suffers from equity-like drawdowns. But for investors with a mandate to always be in equities, relative momentum gave 200 basis points more in annual return than the S&P 500.

Absolute momentum had 90 basis points more in annual return than the S&P 500. Its lower return than relative momentum is due to occasional whipsaws and lags in getting in or out of equities at their turning points. But absolute momentum gave reduced drawdowns.

There is a synergy in combining both types of momentum. The combined whole is greater than the sum of the parts. If you reduce bear market exposure using absolute momentum, you gain more from relative momentum in bull markets. For example, the average bear market loss of the S&P 500 since 1950 was 33%. It takes a 50% gain to recoup that size loss, and the stock market gains about 10% per year. So, it can take 5 years on average to reach breakeven. If absolute momentum substantially reduces bear market losses, then bull market gains become new profits instead of making up losses. That is why GEM shows an impressive 440 basis point increase in annual return above the S&P 500 from 1950 until now, versus 200 basis points for relative momentum and 90 basis points for absolute momentum. As with absolute momentum, GEM returns were achieved with considerably reduced downside exposure.

Here are tables showing how absolute and relative momentum performed during bull and bear market cycles.


BULL MARKETS
S&P 500
Abs Mom
GEM
Jan 1950- Dec 1961
647.7
608.3
1014.6
Jul 1962- Nov 1968
143.7
66.7
58.0
Jul 1970- Dec 1972
75.6
47.2
84.0
Oct 1974- Dec 1980
198.3
91.6
103.3
Aug 1982-Aug 1987
279.7
246.3
569.2
Dec 1987- Aug 2000
816.6
728.4
730.5
Oct 2002-Oct 2007
108.3
72.4
181.6
Mar 2009-Dec 2017
338.7
177.4
142.3
AVERAGE
326.1
254.8
360.4


BEAR MARKETS
S&P 500
Rel Mom
GEM
Jan 1962- Jun 1962
-22.8
-18.5
-15.7
Dec 1968- Jun 1970
-29.3
-13.9
   4.3
Jan 1973- Sep 1974
-42.6
-35.6
 15.1
Dec 1980- Jul 1982
-16.5
-16.9
 16.0
Sep 1987- Nov 1987
-29.6
-15.1
 15.1
Sep 2000- Sep 2002
-44.7
-43.4
 14.9
Nov 2007-Feb 2009
-50.9
-54.6
-13.1
AVERAGE
-33.8
-28.3
   0.9

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

Absolute momentum gave less profit than the S&P 500 during bull markets. But dual momentum-based GEM produced more profit. Relative momentum by itself suffered nearly the same bear market losses as the S&P 500. But GEM, over the long run, eliminated those losses over this 68 year period.

 Core Versus Satellite


Fama and French call momentum "the premier anomaly." With the growth in factor-based investing, more investors are now willing to add momentum to their portfolios.

Trend following has also been gaining traction. Academic research on trends over the past few years as shown here, has switched from hostility to skepticism to acceptance.

More often than not, those who invest in momentum or trend use it as a satellite rather than as a core holding. This may be due to anchoring or familiarity bias. There can also be a strong home country bias that reduces investing in non-U.S. stocks. Some investors may not yet fully appreciate dual momentum as a more dynamic rather way to diversify. Others might have a long-standing prejudice against timing stock market entries and exits.

For investment professionals, there is also career risk. All strategies that diverge from the market will at times underperform. If you lose money when everyone else is losing money, you will probably hold on to your clients. But all that changes if you are doing something different and then lose money when others do not.

Ironically, the biases that keep investors away from dual momentum are reasons why it works as well as it does. The behavioral explanation of momentum starts with underreaction to relevant information.

You can never be sure of the future, and there will always be tracking error when you deviate from a benchmark portfolio. So we can understand those who are comfortable having multiple investments. Here are some allocation scenarios to consider. They show GEM combined with GAA over the past 68 years.



GEM
75%/25%
50%/50%
25%/75%
 GAA
CAGR
 15.8
 14.4
 13.0
 11.5
10.0
Annual Std Dev
 11.5
 10.4
  9.8
  9.7
 9.8
Sharpe Ratio
 0.96
 0.92
 0.85
0.73
0.57
Worst Drawdown
-17.8
-21.2
-28.1
-34.9
-41.2
Worst 6 Months
-15.7
-14.6
-17.0
-25.3
-33.0
Worst 12 Months
-17.8
-21.2
-24.6
-28.0
-35.7
% of Profit Months
   69
   69
   68
   68
   67

Results are hypothetical, are NOT an indicator of future results, and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Please see our Disclaimer page for more information.

For more details about GEM or dual momentum, see my book.

 [1] Grubel (1968), “Internationally Diversified Portfolios: Welfare Gains and Capital Flows

 [2] Levy & Sarnat (1970), “International Diversification of Investment Portfolios,” Solnik (1974), "Why Not Diversify Internationally Rather Than Domestically?

 [3] Moskowitz (2010), "Momentum Investing: Finally Accessible for Individual Investors," Investments Wealth Monitor